Date of Completion
Fractional Laplacian, s-Harmonic Extension, Traveling fronts, Existence
Field of Study
Doctor of Philosophy
We consider the traveling fronts of the reaction diffusion equations with fractional Laplacian. We show the nonexistence of the traveling fronts in the combustion model with fractional Laplacian in the supercritical case. Our method can be used to give a direct and simple proof of the nonexistence of traveling fronts for the Fisher-KPP nonlinearity. Also we prove the existence and nonexistence of traveling fronts for different ranges of the fractional power in the generalized Fisher-KPP type model.
Huan, Tingting, "Traveling Fronts to Reaction Diffusion Equations with Fractional Laplacians" (2014). Doctoral Dissertations. 462.